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Presentation of Data Test - 26

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Presentation of Data Test - 26
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  • Question 1
    1 / -0

    Directions For Questions

    The sale of salesman in a week are given below in the pie diagram. Study the diagram and answer the following questions, if the total sale due to salesman AA is Rs. 18,000.18,000.

    ...view full instructions

    Find the sales of salesman BB.

    Solution
    $$
    The\quad circle\quad in\quad a\quad pie\quad chart\quad represents\quad { 360 }^{ o }.\\ When\quad Central\quad angle\quad for\quad Salesman\quad A\quad is\quad { 90 }^{ o }\quad \rightarrow \quad Total\quad sales\quad done\quad by\quad Salesman\quad A\quad in\quad 1\quad week\quad is\quad Rs.18000\\ For\quad total\quad angle\quad { 360 }^{ o },\quad totol\quad sale\quad by\quad all\quad =\quad \dfrac { 18000 }{ 90 } \quad \times \quad { 360 }\quad =\quad Rs.\quad 72000\\ Sale\quad by\quad salesman\quad B\quad =\quad \dfrac { 120 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 24000\\ Sale\quad by\quad salesman\quad C\quad =\quad \dfrac { 80 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 16000\\ Sale\quad by\quad salesman\quad D\quad =\quad \dfrac { 70 }{ 360 } \quad \times \quad 72000\quad =\quad Rs.\quad 14000
    $$

  • Question 2
    1 / -0

    Directions For Questions

    The following diagram represents the sectorwise loan amount in crores of Rs. 180180 distributed by a bank. From the information, answer the following question:

    ...view full instructions

    If the dairy sector receives Rs. 2020 crores, then find the total loan disbursed.

    Solution
    Suppose total loan =x= x
    Part of dairy will be =x×(40360)= x\times \left (\dfrac {40}{360}\right)
    x×(40360)=20\Rightarrow x\times \left (\dfrac {40}{360}\right) = 20
    x=20×(36040)\Rightarrow x = 20\times \left (\dfrac {360}{40}\right)
    x=180\Rightarrow x = 180
    So, total loan is 180180 crore Rs.
  • Question 3
    1 / -0

    Directions For Questions

    The sale of salesman in a week are given below in the pie diagram. Study the diagram and answer the following questions, if the total sale due to salesman AA is Rs. 18,000.18,000.

    ...view full instructions

    The salesman with the highest sale is:

    Solution
    In a given pie chart, Salesman B has the greatest angle i.e. 120°120° when compared to other salesmen.
    Also, we know that in a circle, greater the angle of an arc, greater the area.
    \therefore Salesman B has the highest sale.
  • Question 4
    1 / -0

    Directions For Questions

    The sale of salesman in a week are given below in the pie diagram. Study the diagram and answer the following questions, if the total sale due to salesman AA is Rs. 18,000.18,000.

    ...view full instructions

    Find the difference between the highest sale and the lowest sale.

    Solution
    Given:- Sale due to salesman A = 18000
    Here, Sale due to A = area of circle4=18000 \cfrac{\text{area of circle}}{4} = 18000
    Let the radius be r.
    πr24=18000 \Rightarrow \cfrac{\pi r^2}{4} = 18000
    r2=18000.4π \Rightarrow r^2 = \cfrac{18000.4}{\pi}
    Sales due to A is area formed by A
    Area of arc = θ×r22 \cfrac{\theta \times r^2}{2}
    Also, we know that arc with maximum or greatest angle with serve the greatest area.
    \Rightarrow greatest area = highest sale
    Also, arc with smallest angle will serve the smallest area
    \Rightarrow Smallest  area = Lowest sale
    \therefore Highest sale will be due to Salesman B
    and Lowest sale will be due to Salesman D
    Sale due to B = Area covered by B
    =2π3×r22 = \cfrac{\cfrac{2\pi}{3} \times r^2}{2}
    =2π3×2×18000×4π = \cfrac{2\pi}{3 \times 2} \times \cfrac{18000 \times 4}{\pi}
    =24000 24000 Rs
    Sale due to D = Area covered by D
    =7π9×r22 = \cfrac{\cfrac{7\pi}{9} \times r^2}{2}
    =7π9×2×18000×4π = \cfrac{7\pi}{9 \times 2} \times \cfrac{18000 \times 4}{\pi}
    = 1400014000 Rs
    Difference = Highest Sale - Lowest Sale 
    = Sale due to B - Sale due to D = 2400014000=1000024000 - 14000 = 10000

  • Question 5
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    Refer the pie chart and answer.
    To show the distribution of proteins and other dry elements in the human body, the arc of the circle should subtend at the center an angle of:

    Solution
    Percentage of proteins and other dry elements in the body is  (16%+14%)16\% + 14\%) which is equal to 30% 30\%

    \therefore Central angle corresponding to proteins and other dry elements together  =30% of 360=30\% \ of \ 360^\circ
    30100×360\Rightarrow \dfrac{30}{100} \times 360  
    =108=108^\circ
  • Question 6
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    Directions For Questions

    The following pie diagram represents the number of valid votes obtained by four students who contested for school captain. The total of valid votes polled was 720720. Based on the given data answer the following questions :

    ...view full instructions

    By how many votes did the winner defeat the nearest contestant?

    Solution
    Total number of votes =720= 720 
    Nashima was the winner with central angle as 120o{ 120 }^{ o }.
    The next person to get maximum votes was Albert with central angle as 100o{ 100 }^{ o }
    Difference between their angles =120100=20o= 120 -100= { 20 }^{ o } 
    So, the number of votes by which Nashima defeated Albert =20360× 720=40 = \dfrac { 20 }{ 360 }\times  720= 40 votes.
  • Question 7
    1 / -0
    In statistics a suitable graph for representing the partitioning of total into sub parts is?
    Solution
    In statistics a suitable graph for representing the partitioning of total into sub parts is a pie graph.

  • Question 8
    1 / -0
    The adjoining diagram illustrates the information collected about the number of brothers of the boys in a certain group.
    What is the total number of boys in this group ?

    Solution
    Total number of boys =2+5+4+7+3+1=22 = 2 + 5 + 4+7 +3+1 = 22
  • Question 9
    1 / -0

    Directions For Questions

    The sale of salesman in a week are given below in the pie diagram. Study the diagram and answer the following questions, if the total sale due to salesman AA is Rs. 18,000.18,000.

    ...view full instructions

    Find the total sale

    Solution
    The circle in a pie chart represents 360o{ 360 }^{ o }
    When Central angle for Salesman AA is 90o{ 90 }^{ o }
    Total sales done by Salesman AA in 11 week is Rs. 1800018000 
    For total angle 360o{ 360 }^{ o }, total sales by all =1800090 × 360==\dfrac { 18000 }{ 90 }  \times  { 360 }= Rs. $$72000
    $$
  • Question 10
    1 / -0

    Directions For Questions

    The following pie diagram represents the number of valid votes obtained by four students who contested for school captain. The total of valid votes polled was 720720. Based on the given data answer the following questions :

    ...view full instructions

    Nashima had ______ the election.

    Solution
    In the given piechart, we know that Nashima had created the greatest arc in the circle.
    As we know that the arc with the greatest angle covers the greatest area.
    Here, the greatest angle is 120°, which is of for Nashima's vote.
    Thus, Nashima gets the maximum vote.
    \therefore Nashima won the election.
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